Data communications systems face a wide range of performance demands. These demands include bandwidth efficiency, power efficiency, signal-to-noise (SNR) efficiency, and robustness. Bandwidth efficiency refers to successfully communicating data using as little bandwidth as possible. Power efficiency refers to transmitting as much energy per bit as possible for a given amount of consumed power. SNR efficiency refers to successfully communicating data using as little energy per bit as possible. Robustness refers to tolerating a variety of transmission channels characteristics. While conventional system designs often attempt to meet these demands independently of one another, they are interrelated.
Phase shift keying (PSK) represents a class of modulations that do a good job of meeting power efficiency, SNR efficiency, and some robustness demands. Power efficiency is achieved because PSK modulations convey data using phase, but not amplitude, relationships between quadrature components of a digital communication transmission signal. Since amplitude is not modulated, highly efficient class-C amplifiers may be employed in transmitters. SNR efficiency is achieved by using any of a wide variety of conventional coding schemes. One popular coding scheme is concatenated coding. Typically, a block code, such as a Reed-Solomon code, is applied as an outer code, and a convolutional code, such as the well known K=7, rate 1/2 "Viterbi" convolutional code, is applied as an inner code.
Another popular coding scheme is pragmatic trellis coded modulation (PTCM). PTCM has become popular because it allows a single convolutional encoder and decoder to achieve respectable coding gains for a wide range of bandwidth efficiencies (e.g. 1-6 b/s/Hz) and a wide range of higher order coding applications, such as 8-PSK, 16-PSK, 16-QAM, 32-QAM, etc. Accordingly, PTCM addresses both SNR efficiency and robustness. PTCM may be used within a concatenated coding scheme. For lower order coding applications, such as QPSK or BPSK, PTCM offers no advantage because quadrature, complex communication signals provide two independent dimensions (i.e. I and Q) per unit baud interval with which to convey two or fewer symbols per unit interval. PTCM solves some of the robustness demands because a wide range of coding applications can be accommodated with a single set of hardware.
Generally, PTCM conveys "coded" bits with "uncoded" bits during each unit interval. In other words, each phase point of a phase constellation is defined by both coded and uncoded bits. The coded bits receive convolutional encoding and the uncoded bits do not. Regardless of modulation order or type, the convolutional coding parameters are the same for any of a wide range of coding applications.
Unfortunately, the PSK class of modulations exhibit relatively poor bandwidth efficiency and are conventionally unable to resolve some robustness demands, such as rotational invariance. Accordingly, digital communication systems occasionally look to amplitude phase shift keying (APSK) modulation to achieve bandwidth efficiency over PSK modulation.
APSK modulation achieves performance improvements over an otherwise equivalently ordered PSK modulation. APSK modulations convey data using both amplitude and phase relationships between quadrature components of a digital communication transmission signal. A prior art rectilinear APSK (R-APSK) phase constellation 10 is shown in FIG. 1. Constellation 10 and other R-APSK modulations are conventionally referred to as quadrature amplitude modulation (QAM), but will be referred to herein using the generic term "R-APSK" to distinguish them from polar APSK (P-APSK) modulations, discussed below.
R-APSK constellations represent a special class of constellations where one set of symbols is conveyed independently of another set of symbols. In 16 R-APSK (i.e. 16-QAM), two symbols are communicated using I phase constellation axis perturbations and two symbols are communicated using Q phase constellation axis perturbations. Since the I and Q axes are orthogonal, the two sets of symbols have no influence over one another.
PTCM has been adapted to R-APSK constellations with moderate success. Typically, one coded bit and one uncoded bit are conveyed by perturbations about each of the I and Q axes. Unfortunately, conventional R-APSK constellations do not achieve rotationally invariant communication systems without accepting a tremendous degradation in performance (e.g. 4 dB). Without rotational invariance, the duration required for a decoder to achieve synchronization is much longer than with rotational invariance. When rotational invariance is sacrificed, conventional R-APSK constellations achieve acceptable performance, but performance is still not optimized.
FIG. 1 denotes a sub-constellation 12 included in the exemplary 16 R-APSK constellation 10. Sub-constellation 12 shares a common data value for the two coded information bits communicated during any single unit interval. Those skilled in the art will appreciate that constellation 10 actually includes four similar sub-constellations 12, but only one is shown for clarity. FIG. 1 further denotes a single minimum sub-constellation Euclidean distance 14 and a single minimum sub-constellation Euclidean distance 16 for the 16 R-APSK example. Minimum secondary distance 14 is the smallest distance between phase points in constellation 10. Minimum distance 16 is the smallest distance between phase points in any given sub-constellation 12.
The value of these minimum distances has a large influence on bandwidth and SNR efficiencies. One reason R-APSK communication systems do not demonstrate better performance is believed to be that these distances result from discrete, independent I, Q values which dictate the positions of the phase points in constellation 10. For example, constellation 10 is achieved when phase points have I and Q coordinates consisting of all sixteen combinations of .+-.1 and .+-.3, scaled by a factor of 2/(3.sqroot.2). Minimum distance 14 is 2/(3.sqroot.2), and minimum distance 16 is 4/(3.sqroot.2). As a result, the performance of the coded bits are not balanced with the performance of the uncoded bits unless signal-to-noise ratio is held at a single specific value.
Furthermore, conventional applications of PTCM to R-APSK constellations provide an excessive number of phase points at the respective minimum distances from other phase points. For the 16 R-APSK example depicted in FIG. 1, four minimum Euclidean distances 16 exist for each of the four sub-constellations 12, resulting in a total of 16 Euclidean distances 16 in constellation 10. This large number of minimum Euclidean distances 16 causes performance to suffer.
While R-APSK constellations achieve bandwidth efficiency over PSK modulation, they do so at a severe cost in power efficiency. Consequently, R-APSK constellations are particularly undesirably when used on peak power limited channels, such as characterize satellite communications. As illustrated by FIG. 1 for a specific 16 R-APSK constellation, phase points reside in three concentric rings. Peak transmitter power is required to transmit phase points on the outer ring. In random data, only 1/4 of the data are transmitted at this peak power. Accordingly, this transmitter peak power capability is used to transmit only 1/4 of the data, resulting in an inefficient use of the peak power capability. In general, R-APSK constellations require an excessive number of phase point rings for a given number of phase points in the constellation, and this excessive number of rings causes an inefficient use of transmitter power so that an undesirably low amount of power is transmitted per bit on average.
Moreover, transmitter amplifiers introduce AM-AM and AM-PM distortions in the signals they amplify. AM-AM distortions characterize non-linear amplitude variations in an amplifier output signal which occur as a function of input amplitude but are not explained by amplifier gain. AM-PM distortions characterize phase variations in an amplifier output signal which occur as a function of input amplitude. The use of an excessive number of rings in R-APSK for a given number of phase points requires transmitter amplifiers to operate at an excessive number of input amplitude states and causes an excessive amount of AM-AM and AM-PM distortions.
In theory, P-APSK constellations should have superior characteristics to R-APSK constellations, particularly in peak power limited channels. P-APSK constellations can be arranged so that a greater percentage of random data is transmitted using the peak power to achieve transmitter amplifier utilization efficiency. In addition, AM-AM and AM-PM distortions can theoretically be reduced if fewer rings are used to implement a phase constellation when compared to a R-APSK constellation having an equivalent number of phase points.
Unfortunately, conventional P-APSK constellations are not adapted to PTCM communication systems. Accordingly, such constellations have been proposed in either uncoded or in fully coded applications. Uncoded applications apply no convolutional coding to the communicated information bits, and fully coded applications apply convolutional coding to all communicated information bits. Uncoded applications are highly undesirable because they demonstrate significantly degraded performance when compared with equivalent pragmatic or fully coded applications. Fully coded applications are undesirable because they require the use of different convolutional encoders and decoders for different modulation orders.
Likewise, conventional receiver decoders have been unable to adequately adapt to a wide range of modulation types, orders and coding rates, particularly when configured to decode PTCM. For high speed digital communication applications, high data rates dictate that hardware rather than software, be primarily used to encode and decode data. Conventional practices require new hardware to accommodate new convolutional codes, coding rates and phase point constellations. This is an undesirably expensive and time consuming undertaking.
The puncturing of convolutional codes is a conventional technique for increasing a code rate at the expense of code strength. Prior art communication systems have applied puncturing to R-APSK and PSK, PTCM schemes. Punctured codes simply refrain from transmitting a portion of the convolutionally encoded bits between a transmitter and a receiver. Sufficient redundancy is built into the convolutional code that the original uncoded data stream may be reconstructed without communicating the omitted encoded bits. Even though certain encoded bits are not transmitted, they must be compensated for at the receiver. Accordingly erasures are inserted at the receiver for the omitted encoded bits prior to convolutional decoding.
The prior art systems which employ puncturing conventionally insert a constant erasure value that does not vary regardless of any particular received phase state. This technique works acceptably well when the conveyed encoded symbols are independent of one another. However, a cost of independently conveyed encoded symbols is the use inefficient phase constellation configurations for PTCM systems, such as R-APSK.